Question: Simplify; express your answer in exponential form. Assume $k\neq 0, a\neq 0$. $\dfrac{{(k)^{-1}}}{{(k^{2}a^{4})^{5}}}$
To start, try working on the numerator and the denominator independently. In the numerator, we have ${k}$ to the exponent ${-1}$ . Now ${1 \times -1 = -1}$ , so ${(k)^{-1} = k^{-1}}$ In the denominator, we can use the distributive property of exponents. ${(k^{2}a^{4})^{5} = (k^{2})^{5}(a^{4})^{5}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(k)^{-1}}}{{(k^{2}a^{4})^{5}}} = \dfrac{{k^{-1}}}{{k^{10}a^{20}}}$ Break up the equation by variable and simplify. $\dfrac{{k^{-1}}}{{k^{10}a^{20}}} = \dfrac{{k^{-1}}}{{k^{10}}} \cdot \dfrac{{1}}{{a^{20}}} = k^{{-1} - {10}} \cdot a^{- {20}} = k^{-11}a^{-20}$.